Both quantitative and qualitative models can be either deductively or inductively constructed. Deductive modeling requires a priori knowledge of the mechanisms that are responsible for the dynamic system behavior. Using this knowledge, a model can be derived from which system behavior can be deduced. Inductive modeling requires previously measured data records describing the input/output behavior of the system. From this data, possible mechanisms that would explain the observed behavior may be deduced.
Purely inductive quantitative models are hardly ever used. Any quantitative model requires some prior assumption about the model structure. If no other information is available, usually a linear structure is assumed. However, if a linear structure does not explain the observed behavior well, and if nevertheless no structural knowledge is available that can be used for the construction of a quantitative model, a qualitative inductive model may be the right choice. Since inductive models require less information for their construction, qualitative inductive models can be constructed without presupposing structural information.
A general methodology for qualitative inductive modeling of dynamical processes was recently developed [Li and Cellier, 1990]. The approach has been named Fuzzy Inductive Reasoning (FIR). It turns out that FIR models are quite compatible with quantitative deductive models that are respresented through sets of differential and/or difference equations. Thus, mixed models can be constructed whereby the well-understood subsystems can be modeled using quantitative deductive (differential equation) models, whereas the poorly-understood subsystems are described using qualitative inductive (FIR) models [Cellier et al., 1992].
Applications of this methodlogy are manyfold, ranging from biomedical [Nebot et al., 1990] applications to the systematic design of fuzzy controllers [Cellier and Mugica, 1992], [Mugica and Cellier, 1993] and the design of generic fault characterization tools for complex technical processes such as nuclear power plants [de Albornoz and Cellier, 1993] or aircrafts [de Albornoz and Cellier, 1993], and a number of them are described in this tutorial.
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